Hi tracemeek,
As CS 3 was not tested on 10.9.4, there could be an issues while installing CS 3 on Latest Mac due to incompatibility of OS and software.
Please check out the system requirements for CS3 from the link mentioned below.
System Requirements : System requirements | Design Premium
You can certainly try if it works for you. You already have the link to download CS3 : Download CS3 products
I would really appreciate if you could try the download it with different browser or on another machine, which you can carry in a flash drive/pen drive to your new Mac Mini.
If you get "Licensing has stopped working" error.
Make sure that you follow all the steps from : Error "Licensing has stopped working" | Mac OS
Please revert if the problem still persists
Thanks,
Atul Saini